In general, in starting an engine, a pinion which transmits power of a starter to an engine for cranking the engine is pushed out by a solenoid coil so that the pinion is meshed with a ring gear connected to a crankshaft of the engine and thereby cranking of the engine is performed with the use of power of the starter. The starter for an idling stop is configured such that, when a vehicle is stopped temporarily, the pinion is pushed out to be meshed with the ring gear after the engine is brought into a stop state. Here, there may be a case where a driver makes a restart request by suddenly changing his mind although he firstly wanted to stop his vehicle temporarily. However, even when such a restart request is made during a fall of the rotation of the engine, a restart is not performed until the rotation of the engine is brought into a stop state and a time lag occurs before the restart is performed.
In view of the above-mentioned circumstance, in Japanese patent 4214401 (patent document 1), when a restart request is made during a fall of the rotation of an engine, power is supplied to a starter so as to idle a pinion, rotational speeds of the pinion and a ring gear are respectively detected, and a pinion is pushed out to be meshed with a ring gear at a point of time that the respective rotations synchronize with each other thus restarting the engine rapidly. In Japanese patent 4237150 (patent document 2), a signal outputting portion having a convex and concave shape is formed on an outer peripheral surface of a cylindrical outer peripheral wall of a clutch outer of a starter-use one-way clutch, and a rotational speed of a crankshaft is detected by a signal detection sensor.